A remark on the orthogonality of a class of bidimensional nonseparable wavelets (Q812453)

The author provides a necessary condition and an optimal sufficient condition on conjugate quadrature filters that associate with orthonormal scaling functions with dilation \(M: =\left(\begin{smallmatrix} 1& 1\\ 1 & -1\end{smallmatrix}\right)\). For one-dimensional conjugate quadrature filters, similar results are established in [\textit{A. Cohen} and \textit{Q. Sun}, SIAM J. Math. Anal. 24, No. 5, 1355--1360 (1993; Zbl 0792.42022)], [\textit{R. Q. Jia} and \textit{J. Z. Wang}, Proc. Am. Math. Soc. 117, No. 4, 1115--1124 (1993; Zbl 0770.42018)] and [\textit{X. Zhou} and \textit{W. Su}, Appl. Comput. Harmon. Anal. 8, No. 2, 197--202 (2000; Zbl 0942.42020); ibid. 9, No. 2, 120--127 (2000; Zbl 0963.42020).